Breaking JIT optimisations with reflection

When fiddling with unit tests for a highly-concurrent singleton class I stumbled upon the following weird behaviour (tested on JDK 1.8.0_162):

private static class SingletonClass {
    static final SingletonClass INSTANCE = new SingletonClass(0);
    final int value;

    static SingletonClass getInstance() {
        return INSTANCE;
    }

    SingletonClass(int value) {
        this.value = value;
    }
}

public static void main(String[] args) throws NoSuchFieldException, IllegalAccessException {

    System.out.println(SingletonClass.getInstance().value); // 0

    // Change the instance to a new one with value 1
    setSingletonInstance(new SingletonClass(1));
    System.out.println(SingletonClass.getInstance().value); // 1

    // Call getInstance() enough times to trigger JIT optimizations
    for(int i=0;i<100_000;++i){
        SingletonClass.getInstance();
    }

    System.out.println(SingletonClass.getInstance().value); // 1

    setSingletonInstance(new SingletonClass(2));
    System.out.println(SingletonClass.INSTANCE.value); // 2
    System.out.println(SingletonClass.getInstance().value); // 1 (2 expected)
}

private static void setSingletonInstance(SingletonClass newInstance) throws NoSuchFieldException, IllegalAccessException {
    // Get the INSTANCE field and make it accessible
    Field field = SingletonClass.class.getDeclaredField("INSTANCE");
    field.setAccessible(true);

    // Remove the final modifier
    Field modifiersField = Field.class.getDeclaredField("modifiers");
    modifiersField.setAccessible(true);
    modifiersField.setInt(field, field.getModifiers() & ~Modifier.FINAL);

    // Set new value
    field.set(null, newInstance);
}

The last 2 lines of the main() method disagree on the value of INSTANCE - my guess is that JIT got rid of the method completely since the field is static final. Removing the final keyword makes the code output correct values.

Leaving aside your sympathy (or lack thereof) for singletons and forgetting for a minute that using reflection like this is asking for trouble - is my assumption correct in that JIT optimisations are to blame? If so - are those limited to static final fields only?